In an action-adventure film, the hero is supposed to throw a grenade from his ca

Question

In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 99.0 km/h, to his enemy's car, which is going 130 km/h . The enemy's car is 13.4 m in front of the hero's when he lets go of the grenade.

Part A

If the hero throws the grenade so its initial velocity relative to him is at an angle of 45 above the horizontal, what should the magnitude of the initial velocity be? The cars are both traveling in the same direction on a level road. You can ignore air resistance.

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Part B

Find the magnitude of the velocity relative to the earth.

In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 99.0 km/h, to his enemy's car, which is going 130 km/h . The enemy's car is 13.4 m in front of the hero's when he lets go of the grenade.

Part A

If the hero throws the grenade so its initial velocity relative to him is at an angle of 45 above the horizontal, what should the magnitude of the initial velocity be? The cars are both traveling in the same direction on a level road. You can ignore air resistance.

v0 =   km/h  

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Part B

Find the magnitude of the velocity relative to the earth.

v0 =   km/h  

Explanation / Answer

Let the intital velocity be v.
Horizontal component,vx = v*cos(45)
Vertical component,vy = v*sin(45)

Horizontal distance = 13.4 m
sy = vy * t + 1/2*ay*t^2
0 = v*sin(45) *t - 1/2 * 127008 * t^2
t = v*sin(45) / 127008 --------1

Horizontal distance cover in this time, = v*cos(45) * t
This distance should be equal to = (130 - 99.0) * t + 13.4/1000

(130 - 99.0) * t + 13.4/1000  = v*cos(45) * t
((130 - 99.0) * v*sin(45)) / 127008 + 13.4/1000  = (v*cos(45) *v*sin(45)) / 127008
0.00017 v + 0.0134 = 3.94 * 10^-6 v^2
v = 83.75 km/h
Magnitude of initial velocity, v = 83.75 km/hr


(2)
Magnitude of velocity relative to eartth,
Vx = 99.0 + 83.75 * cos(45) = 158.22 km/hr
Vy = 83.75 * sin(45) = 59.22 km/hr

V = sqrt(vx^2 + vy^2) = sqrt(158.22^2 + 59.22^2)
V = 168.9 km/hr

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